Examples of board games in which gameplay is very light would be games like Lands of Galzyr, or Roll Player Adventures. Both of these games are full of "fail forward" mechanics, so that if you do badly in gameplay (whether by bad luck or bad skill), you still move the story forward all the time. It is impossible to reach a moment where through a death spiral in gameplay you "lose the game" and need to start over. These are great games for families or casual gamers, but the game mechanics will feel very light and "too easy" for more veteran gamers. Still, I sometimes do enjoy such lighter fare.

At the other extreme are games which nearly fall of the edge of still being considered narrative games, because the amount of story you get is rather small compared to the amount of gameplay. My worst example in recent time was Bardsung, where you only get a paragraph or so of story after every complete dungeon crawl (and the repetitive dungeon crawls aren't fun enough to play anyway). But even a great game like Gloomhaven has far more gameplay than story, and the 95 scenarios (60+ to get through a campaign once) are probably too much for most people, so very few players will get to see the end of the story.

My wife and me are currently playing Tainted Grail: The Fall of Avalon on easy "story mode". The problem with Tainted Grail is that exploration takes time and resources; so if by bad luck or bad skill you get into a bad loop of gameplay in which you have no time and no resources, but just make move after move just trying to stay alive. There are even rules for death and complete failure in the standard rules of Tainted Grail, which would ask you to start over from the beginning. However, there are also alternative rules to ignore death and failure, and just keep playing. Basically in Tainted Grail you need to tune the rules to a level of difficulty in which there are enough time and resources left to keep moving the story forward. And even the devs think that the standard rules are a bit too heavy on the gameplay loops, and are working on 2.0 rules to make those a bit easier and less time-consuming. The 7th Continent has similar problems, where a struggle for survival can become so overwhelming as to stop story advancement. Note that of these two, Tainted Grail has the much better story, although I'd say that The 7th Continent has more interesting gameplay. It really depends what you are playing these games for.

A great game with a great balance between gameplay and story is Sleeping Gods. It has just enough worker placement / resource management and character development gameplay to make the gameplay interesting enough for standard gamers, while never getting into the way of the large amount of story content. But Sleeping Gods is clearly primarily a narrative game, and the gameplay comes second. While also nicely balanced in its own way, in Clank!: Legacy - Acquisitions Incorporated the gameplay comes first, and the story is more of a side-show that is there to explain the gameplay changes in the legacy elements. It is more of a story-enhanced deckbuilding game than a narrative board game.

While the balance between gameplay and story is important, even the best balance can't help you if the story is bad or simply not interesting for you. I didn't buy Etherfields because the horror/dream theme of the game didn't appeal at all to me. And I am still on the fence on ISS Vanguard, because I usually prefer fantasy to science fiction. In Destinies you play through a campaign of five stories in the base game, and while we liked the early ones, we felt that the quality of the story decreased markedly over the course of the campaign, and the 5th story was just a confusing mess that was no fun at all. Unfortunately that is the sort of information that even most reviewers never get to, especially not if they reviewed a Kickstarter prototype which only contained the first story or two.

I am buying a lot of narrative board games, because those I can most easily play with my wife. Narrative games frequently shine with lower player numbers, solo or two players, because of the difficulty of getting everybody listening and involved in the story at higher player counts. Even with two players we prefer games in which the story has some app support for voice narration, rather than one of us having to read aloud for the other. At their best, narrative board games are a great way for me and my wife to interactively experience a story together.